3. the copernican revolution and newton’s revolution or , the revolution revolution:

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Ast 1001 lecture 3 -- 2007 Sept 11 (kd) 3. The Copernican Revolution and Newton’s Revolution or , The Revolution Revolution: what revolves about what, and why? Astronomy 1001, Sept 2007 – Prof. K. Davidson

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Astronomy 1001, Sept 2007 – Prof. K. Davidson. 3. The Copernican Revolution and Newton’s Revolution or , The Revolution Revolution: what revolves about what, and why ?. Principal players Nicolaus Copernicus (1473 – 1543) Galileo Galilei (1564 – 1642) - PowerPoint PPT Presentation

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Page 1: 3.  The Copernican Revolution and Newton’s Revolution or , The  Revolution  Revolution:

Ast 1001 lecture 3 -- 2007 Sept 11 (kd)

3. The Copernican Revolutionand Newton’s Revolution

or,The Revolution Revolution:what revolves about what,

and why?

Astronomy 1001, Sept 2007 – Prof. K. Davidson

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Ast 1001 lecture 3 -- 2007 Sept 11 (kd)

Principal players

Nicolaus Copernicus (1473 – 1543)

Galileo Galilei (1564 – 1642)

Johannes Kepler (1571 – 1630)

Isaac Newton (1642 – 1727)

Notable supporting roles

Thomas Digges (1546 – 1595)

Tycho Brahe (1546 – 1601)

René Descartes (1596 – 1650)

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Before Copernicus: GEOCENTRIC universe

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CLAUDIUS PTOLEMY’s mathematical theory

from c. 140 during the Roman Empire:perfect circles, epicycles, etc.

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COPERNICUS’ theory, around 1530:

Heliocentric, but otherwise much likePtolemy’s universe: celestial sphere,planets moved in perfect circles and epicycles, etc., -- pretty complicated.

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1530 – 1610: WHICH WAS RIGHT? Ptolemy’s geocentric universe vs. Copernicus’ heliocentric universe

There was no obvious way to decide,

until GALILEO and KEPLER settled the

question in two very different ways

during the years 1600 – 1620.

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Meanwhile (around 1570?), Thomas Digges realized something tremendouslyimportant:

If Earth moves around the Sun,then the stars might be likethe Sun but very, very far away!

-- Infinite space instead of acelestial sphere, and maybe each star has its own planets.

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GALILEO used small telescopes to make several critical discoveries:

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1. The Moon has mountains andsurface features, like Earth.

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2. Jupiter has four satellites = moons.

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3. Venus shows a complete set of phases from “crescent” to “full”.

When “full”, it’s obviously much farther away.

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Galileo’s discoveries: 1. Surface features on the Moon 2. Jupiter’s moons 3. “Full” phases of Venus

None of these made sense in Ptolemy’s theory, but they were all perfectly OK in Copernicus’ universe. The phases of Venus are especially decisive.

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(Parenthetically, mention Galileo’s troubles with the Church – basically amatter of internal politics in the Vatican.)

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Johannes KEPLER

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TYCHO BRAHE

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From 1572 to about 1599, Tychoobserved the motions of the planetswith far better precision than anyonehad ever done before.

He had good reasons to doubt BOTHPtolemy’s and Copernicus’ scenarios.He tried to invent an alternative, the“Tychonic theory”.

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Kepler started by assuming that Earth moves around the Sun. But he didn’tassume anything about epicycles, orperfect circles.

Instead he decided to use trigonometryto find the real path of Mars in space.

(Why Mars? -- Because Tycho had observed Mars many, many times over almost 30 years.)

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Kepler’s triangulation of Mars (1600—1610), using Tycho’s earlier observations

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In almost 10 years of calculations, Kepler discovered a fact that would have big consequences later:

The orbit of Mars is an ellipse with the Sun at one focus.

Next we’ll see what this means.

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AN ELLIPSE IS A FLATTENED CIRCLE.

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ELLIPSE, continued

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Two more words: PERIHELION and APHELION

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Kepler noticed that Mars moves fasternear perihelion, slower near aphelion.

On closer inspection he found a rulethat describes the variations in speedat all times.

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KEPLER’S SECOND LAW

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“EQUAL AREAS IN EQUAL TIMES”

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( In reality the planets’ orbits are almost circular. Here’s a scale drawing of Mars’ orbit.)

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Finally, Kepler found a rule that relates the speeds of different planets.

If P = orbital period (“year”) and a = average distance from Sun, then

P 2 / a 3 = the same number for

all the planets (but not the Moon)

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Example ---

Earth: P = 1 year, a = 1 AU (“astronomical unit”),

P 2 / a 3 = 1 / 1 = 1.00. Jupiter: P = 11.86 years, a = 5.20 AU,

P 2 / a 3 = 140.7 / 140.6 = 1.00.

-- It also works for Mercury, Venus, Mars, and Saturn.

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KEPLER’S LAWS FOR THE PLANETS

1. Each orbit is an ellipse, with the

Sun

at one focus*

2. Equal areas in equal times

3. Period squared = radius cubed

* (Note: the orbits aren’t aligned)

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Kepler’s“Rudolphine Tables”

-- very accurate predictions

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KEPLER’S LAWS

Why do they work? -- The

question

that led to modern physics

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1620 — 1665: Kepler’s laws were obviously right, but only a few

peopletried to understand why.

In those days, “why?” was almosta new type of question in science.

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DESCARTES (1596 – 1650): “Vortex” theory

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Isaac Newton (1642 – 1727)

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Newton’s

crucial

“thought experiment”

(1665)

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Brief digression ...

A VECTOR IS A QUANTITY THAT HAS A DIRECTION IN SPACE.

examples: ** POSITION ** ** VELOCITY ** ** ACCELERATION **

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The Moon’s orbit around Earth

R = 384000 km = about 60 x (radius of Earth),

V = 1160 km/hr = 320 m/s.

So the required acceleration toward earth is

A = V 2 / R = 0.027 cm / s / s.

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Moon’s acceleration toward Earth isabout 0.027 cm / s / s.

So what? -- Our acceleration towardEarth is g = 980 cm / s / s. Newtonnoticed that these have the ratio3600.

60 x farther makes gravity weaker by a factor of 3600 x.

This is obviously 60 x 60 = 60 2 !

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“Newton’s second law”: force = M x A .

His law of gravity:

( attractive force between M and m )

= G x M x m / (distance) 2 .

For instance, 3 x farther makes it 9 x

weaker.

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THE “INVERSE SQUARE LAW” OF GRAVITY WAS ENOUGH TO EXPLAIN KEPLER’S LAWS!

1. Orbits are ellipses, Sun at one focus

2. Equal areas in equal times

3. Period squared = radius cubed

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NEWTON’S REVOLUTION WAS AS IMPORTANT AS COPERNICUS’.

There are “laws of physics” that apply

everywhere, from this room to the

edge

of the universe. In 1680 this was a

breathtaking new idea!

It led to modern physical science.

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Mention Newton’s influence on the following century -- “the age of reason”, at least for philosophers.

His historical importance was recognized in his own time -- arguably “the most important man in the world”, outranking even Louis XIV.

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Next time: the amazing diversity of orbital behavior

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